Preface
We have made substantial changes in this edition ofIntroduction to Mathematical
Statistics. Some of these changes help students appreciate the connection between
statistical theory and statistical practice while other changes enhance the develop-
ment and discussion of the statistical theory presented in this book.
Many of the changes in this edition reflect comments made by our readers. One
of these comments concerned the small number of real data sets in the previous
editions. In this edition, we have included more real data sets, using them to
illustrate statistical methods or to compare methods. Further, we have made these
data sets accessible to students by including them in the free R packagehmcpkg.
They can also be individually downloaded in an R session at the url listed below.
In general, the R code for the analyses on these data sets is given in the text.
We have also expanded the use of the statistical software R. We selected R
because it is a powerful statistical language that is free and runs on all three main
platforms (Windows, Mac, and Linux). Instructors, though, can select another
statistical package. We have also expanded our use of R functions to compute
analyses and simulation studies, including several games. We have kept the level of
coding for these functions straightforward. Our goal is to show students that with
a few simple lines of code they can perform significant computations. Appendix B
contains a brief R primer, which suffices for the understanding of the R used in the
text. As with the data sets, these R functions can be sourced individually at the
cited url; however, they are also included in the packagehmcpkg.
We have supplemented the mathematical review material in Appendix A, placing
it in the documentMathematical Primer for Introduction to Mathematical Statistics.
It is freely available for students to download at the listed url. Besides sequences,
this supplement reviews the topics of infinite series, differentiation, and integra-
tion (univariate and bivariate). We have also expanded the discussion of iterated
integrals in the text. We have added figures to clarify discussion.
We have retained the order of elementary statistical inferences (Chapter 4) and
asymptotic theory (Chapter 5). In Chapters 5 and 6, we have written brief reviews
of the material in Chapter 4, so that Chapters 4 and 5 are essentially independent
of one another and, hence, can be interchanged. In Chapter 3, we now begin the
section on the multivariate normal distribution with a subsection on the bivariate
normal distribution. Several important topics have been added. This includes
Tukey’s multiple comparison procedure in Chapter 9 and confidence intervals for
the correlation coefficients found in Chapters 9 and 10. Chapter 7 now contains a
xi